A simple single degree of freedom model of a car traveling over a rough road is

Question

A simple single degree of freedom model of a car traveling over a rough road is shown in Figure 1. The vibration is in the vertical direction. The road surface varies as a cosine curve with an amplitude of Y = 0.1m and wavelength 5m. The vehicle has a mass of m kg and the suspension system has a spring constant of k kN/m and a damping ratio of ? = 0.5. Where V= 35km/hr, m=1060kg, k=478kN/m

Evaluate the following:

A. Find the frequency of the base excitation, in rad/s, if the vehicle is traveling at V km/hour.

B. Find the natural frequency of the system.

C. Find the frequency ratio due to the excitation force on the system.

D.What is the critical velocity of the car in km/hour. Critical velocity is the velocity at which the frequency ratio is 1.

E. Find the displacement amplitude of the car.

F. Find the magnitude of the force transmitted to the car in N.

Explanation / Answer

Y = 0.1m wavelength=L=5m damping ratio of = 0.5. Where V= 35km/hr, m=1060kg, k=478kN/m
a)let L be the length covered
hence: =2v/L

b)natural frequency of the system=n=(k/m)

c)X/Y=(1+(2r)2)/(1-r2)2+(2r)2 =>5/.1=(1+(r)2)/(1-r2)2+(r)2

solving for r=0.707=/n

d)critical velocity =>=n=(k/m)

hence:2v/L=(k/m) =>v=0.534km/hr

e)X=Y[(1+(2r)2)/(1-r2)2+(2r)2]

f)X''|max=2X

force=m.X''|max

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